In computed tomography (CT) the goal is to reconstruct the distribution of the x-ray attenuation coefficient ƒ inside the object being scanned. Local tomography (LT) computes not ƒ, but Bƒ, where B is some operator that enhances singularities of ƒ. In two dimensions (2D), B is an elliptic pseudo-differential operator (PDO) of order one as described by A. Katsevich, “Local Tomography for the Generalized Random Transform”, SIAM Journal on Applied Mathematics, Vol. 57, no. 4 (1997) pp. 1128-1162, Kuchment et al., “On local Tomography”, Inverse Problem 11 (1995), pp. 571-589, A. Ramm and A. Katsevich, “The Random Transform and Local Tomography”, CRC Press, Boca Raton, Fla., 1996 and A. G. Ramm, “Necessary and Sufficient Conditions for a PDO to be a local tomography operator”, Comptes Rend Acad. Sci., Paris 332 (1996) pp. 613-618. In the cone beam setting (three dimensions) a LT function is denoted by gΛ. The corresponding operator B: ƒ→gΛ is much more complicated than in 2D. It preserves the so-called visible (or, useful) singularities and creates non-local artifacts. Unfortunately, the strength of these artifacts is the same as that of the useful singularities of gΛ as described in A. Katsevich “Cone Beam Local Tomography”, SIAM Journal on Applied Mathematics (1999), pp. 2224-2246 and D. Finch et al, “Microlocal analysis of the X-ray transform with sources on a curve”, Inside out: Inverse Problems and Applications, Cambridge Univ. Press, (2003) pp. 193-218.